The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters -- XI. The horizontal branch in NGC\,6388 and NGC\,6441

Abstract: The Hubble Space Telescope UV Legacy survey of Galactic Globular Clusters (GC) is characterising many different aspects of their multiple stellar populations. The "Grundahl-jump" (G-jump) is a discontinuity in ultraviolet brightness of blue horizontal branch (HB) stars, signalling the onset of radiative metal levitation. The HB Legacy data confirmed that the G-jump is located at the same T${eff}$ ($\simeq$11,500 K) in nearly all clusters. The only exceptions are the metal-rich clusters NGC 6388 and NGC 6441, where the G-jump occurs at T${eff}\simeq$13-14,000K. We compute synthetic HB models based on new evolutionary tracks including the effect of helium diffusion, and approximately accounting for the effect of metal levitation in a stable atmosphere. Our models show that the G-jump location depends on the interplay between the timescale of diffusion and the timescale of the evolution in the T${eff}$ range 11,500 K$\lessapprox$T${eff}\lessapprox$14,000 K. The G-jump becomes hotter than 11,500 K only for stars that have, in this T$_{eff}$ range, a helium mass fraction Y>0.35. Similarly high Y values are also consistent with the modelling of the HB in NGC 6388 and NGC 6441. In these clusters we predict that a significant fraction of HB stars show helium in their spectra above 11,500 K, and full helium settling should only be found beyond the hotter G-jump.